Modal logic via group homomorphisms defines cyclic subgroup membership, cyclicity, torsion, and finite generation; the homomorphic modal theory of finitely presented groups is computably isomorphic to true arithmetic.
Modal Model Theory
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Modal group theory: homomorphisms
Modal logic via group homomorphisms defines cyclic subgroup membership, cyclicity, torsion, and finite generation; the homomorphic modal theory of finitely presented groups is computably isomorphic to true arithmetic.